Some observations on the use of discriminant analysis in ecology

The application of discriminant analysis in ecological investigations is discussed. The appropriate statistical assumptions for discriminant are illustrated, and both classification and group separation approaches are outlined. Three assumptions that are crucial in ecological studies are discussed at length, and the consequences of their violation are developed. These assumptions are: (1) equality of dispersions, (2) identifiability of prior probabilities, and (3) precise and accurate estimation of means and dispersions. The use of discriminant functions for purposes of interpreting ecological relationships is also discussed. It is suggested that the common practice of imputing ecological _meaning to the signs and magnitudes of coefficients be replaced by an assessment of _structure coefficients. Finally, the potential and limitations of representation of data in canonical space are considered, and some cautionary points are made concerning ecological interpretation of patterns in canonical space.